We study transport length scales in carbon nanotubes and graphene ribbons under the influence of Anderson disorder. We present generalized analytical expressions for the density of states, the elastic mean free path and the localization length in arbitrarily structured quantum wires. These allow us to explore energies away from the Fermi level and in particular to analyze the electrical response near the van Hove singularities and around the edge state in graphene ribbons. Comparing with the results of numerical simulations, we demonstrate that both the diffusive and the localized regime are well represented by the analytical approximations over a wide range of the energy spectrum. In nanotubes, we find that the effectivity of disorder scales down with increasing diameter even under consideration of multiple scattering and additional conduction channels. In graphene ribbons, we find that the zigzag edge state causes a strong reduction of the localization length in a wide energy range around the Fermi level.